Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been ad...

In the paper we present a new evolutionary algorithm for induction of regression trees. In contrast to the typical top-down approaches it globally searches for the best tree structure, tests at internal nodes and models at the leaves. The general structure of proposed solution follows a framework of evolutionary algorithms with an unstructured population and a generational selection. Specialize...

Motivated by the desire to extend fast randomized techniques to nonlinear lp regression, we consider a class of structured regression problems. These problems involve Vandermonde matrices which arise naturally in various statistical modeling settings, including classical polynomial fitting problems, additive models and approximations to recently developed randomized techniques for scalable kern...

A modification of the classical technique of Prony for fitting sums of exponential functions to data is considered. The method maximizes the likelihood for the problem (unlike the usual implementation of Prony’s method, which is not even consistent for transient signals), proves to be remarkably effective in practice, and is supported by an asymptotic stability result. Novel features include a ...

Constrained multidimensional scaling was put on a firm theoretical basis by Jan De Leeuw and Willem Heiser in the 1980's. There is a simple method of fitting, based on distance via innerproducts, and a numerically more complicated one that is truly based on least-squares on distances. The unconstrained forms are known as principal coordinate analysis and nonmetric multidimensional scaling, resp...

Solving non-binary constraint satisfaction problems, a crucial challenge today, can be tackled in two different ways: translating the non-binary problem into an equivalent binary one, or extending binary search algorithms to solve directly the original problem. The latter option raises some issues when we want to extend definitions written for the binary case. This paper focuses on the well-kno...

The energy conditions of Einsteinian gravity (classical general relativity) do not require one to fix a specific equation of state. In a Friedmann-Robertson-Walker universe where the equation of state for the cosmological fluid is uncertain, the energy conditions provide simple, model-independent, and robust bounds on the behavior of the density and look-back time as a function of red shift. Cu...

In this paper, explicit amplitude and frequency expressions for a Cellular Neural Network with an Opposite-Sign Template (CNN-OST) under oscillation condition are derived and a novel inductorless oscillator circuit with negative feedbacks, based on this simple structure is designed and implemented. The system is capable of generating quasi-sine signals with tuneable amplitude and frequency whic...

In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. More...